After firing a money-management firm for poorly handling the city’s pension funds in 2010, Comptroller John Liu agreed on a separate contract with the same company while bypassing the standard competitive-bidding process, The Post has learned.

Liu awarded Boston-based Acadian Asset Management an $8.37 million contract extension to continue handling certain aspects of the city’s pension funds several weeks ago, according to city records. Acadian first received the contract in 2005.

In June 2010, Liu fired Acadian — which had a separate contract to manage $646 million for three of the city’s five pension funds — over “poor performance” of those funds after the firm reported a 19 percent loss.

“It’s a large investment company, so they have a number of different areas where they focus on, and these two are totally different from one another,” said Liu’s spokesman, Michael Loughran.

Liu picked Acadian without selecting a contractor from among competitive bidders. Such bids are standard city procedure, which he has railed against Mayor Bloomberg for sidestepping.

Instead, Liu used a little-known policy called “innovative procurement,” which allows him to select pension-fund managers faster and without certain restrictions of the traditional process.

Over the past two years, he has awarded more than $67 million in no-bid contracts.

Loughran said innovative procurement, which Liu recently started using, saves time and allows the comptroller to seek out talented money managers who may not have responded to the original “request for proposal” that every city agency publishes when seeking a contractor.

It frees Liu from the restrictions of competitive bidding, and allows his pension team to use industry databases to select from a wider pool, Loughran said.

“[It] also reduces administrative requirements for firms relating to submission of a formal RFP [request for proposal] response, which should be helpful to smaller firms in particular. The Comptroller’s Office anticipates testing this pilot process in solicitations for other asset classes over the coming months,” Loughran said.

Liu, a Democrat, has expressed interest in running for mayor next year, although he remains under a cloud as federal authorities continue to investigate his campaign finances.

So far, the feds have arrested two people in connection with the ongoing probe.